Nuprl Lemma : eclass0-bag-program_wf
∀[Info,B,C:Type]. ∀[X:EClass(B)]. ∀[F:Id ⟶ bag(B) ⟶ bag(C)]. ∀[Xpr:LocalClass(X)].
(eclass0-bag-program(F;Xpr) ∈ LocalClass(eclass0-bag(F;X))) supposing
((∀i:Id. ((F i {}) = {} ∈ bag(C))) and
valueall-type(C))
Proof
Definitions occuring in Statement :
eclass0-bag-program: eclass0-bag-program(f;pr),
eclass0-bag: eclass0-bag(f;X),
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
Id: Id,
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T,
empty-bag: {},
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
local-class: LocalClass(X),
sq_exists: ∃x:{A| B[x]},
eclass0-bag-program: eclass0-bag-program(f;pr),
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
eclass0-bag: eclass0-bag(f;X),
class-ap: X(e),
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
ext-eq: A ≡ B,
hdf-compose0-bag: hdf-compose0-bag(f;X),
top: Top,
mk-hdf: mk-hdf(s,m.G[s; m];st.H[st];s0),
hdf-ap: X(a),
hdf-run: hdf-run(P),
hdf-halt: hdf-halt(),
hdf-halted: hdf-halted(P),
ifthenelse: if b then t else f fi ,
isr: isr(x),
bfalse: ff,
pi2: snd(t),
callbyvalueall: callbyvalueall,
has-value: (a)↓,
has-valueall: has-valueall(a),
btrue: tt,
pi1: fst(t)
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B)]. \mforall{}[F:Id {}\mrightarrow{} bag(B) {}\mrightarrow{} bag(C)]. \mforall{}[Xpr:LocalClass(X)].
(eclass0-bag-program(F;Xpr) \mmember{} LocalClass(eclass0-bag(F;X))) supposing
((\mforall{}i:Id. ((F i \{\}) = \{\})) and
valueall-type(C))
Date html generated:
2016_05_17-AM-09_05_08
Last ObjectModification:
2015_12_29-PM-03_36_55
Theory : local!classes
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